The efficient representation of volumetric meshes is a central problem in scientific visualization. The difference in performance between most visualization algorithm for rectilinear grids and for unstructured mesh is mostly due to fundamental difference in efficiency of their representations. In Computer Graphics the gap in performance between 2D rectilinear grids and unstructured mesh has been overcome with the development of representation schemes based on the concept of subdivision surfaces. This gap has not been bridged in the volumetric cases which is fundamental interest for Scientific Visualization. In this paper we introduce a slow-growing volumetric subdivision scheme for meshes of any topology, any intrinsic dimension and composed of a general type of polyhedral cells.